1. Field of the Invention
The invention relates to a determination of a model of a system, which model includes plural partial models.
2. Description of the Related Art
A determination of such a model is known from Bartholomew et al., Latent Variable Models and Factor Analysis, Charles Griffin, 1987. In this model with partial models (a so-called statistical probability model with a hidden variable y), a probability distribution P for a state x, which state x is described by continuous state quantities xi with xi ∈ R, is described by:                                           P            ⁡                          (                              x                ❘                Θ                            )                                ≡                                    ∑              j                        ⁢                                                   ⁢                                          P                ⁡                                  (                                                            x                      ❘                      y                                        ,                    Θ                                    )                                            ⁢                              P                ⁡                                  (                                      y                    ❘                    Θ                                    )                                                                    ,                            (        1        )            wherein Θ denotes a parameter of the model, i denotes an index for a state quantity, j denotes the number of the partial models, P(a|b) denotes a conditional probability of a variable a under the condition of a variable b, and       ∑    j    ⁢      (    …    )  denotes a summation over the j partial models.
In this model, the probability distribution P(x|y,Θ) of a partial model j is described by using a Gaussian distribution of the formP(x|y, my, σ)∝exp {1/22}  (2)where my denotes a mean, a denotes a variance, exp( . . . ) denotes an exponential function, and P(a|b) denotes a conditional probability of a variable a under the condition b.
The model known from Bartholomew et al. is trained in a training phase so that state quantities are determined on a real system at predetermined times k, and the state quantities for one of the predetermined times k are respectively combined to a training datum. A plurality of such training data form a training data set.
The model is trained with the training data set. An overview of different training methods is likewise to be found In Bartholomew et al. and Tanner et al., Tools for Statistical Inference, Springer, 1996.
In the training phase, usually the following cost function L, a logarithmic likelihood, is minimized:                               L          ⁡                      (            Θ            )                          =                              ∑            i                    ⁢                      log            ⁡                          (                              P                ⁡                                  (                                                            x                      k                                        ❘                    Θ                                    )                                            )                                                          (        3        )            where xk denotes a training datum, Θ a parameter to be matched in the training, log ( . . . ) a logarithm function, and P(xk|Θ) a conditional probability of the training datum xk under the condition of the parameter Θ. The minimization of the logarithmic likelihood usually takes place by the use of an Expectation-Maximization method (EM algorithm), as is known from Tanner et al.
A system for the transmission of data between interconnected computers is known from Fundamentals for the World Wide Web, obtainable on Mar. 16, 1999 under: http:l/www.w3.org/. The components of this system are portions of a communication network, the so-called World Wide Web (WWW).
The communication network connects individual computers together such that the computers can exchange data according to a predetermined transmission protocol, the “Transmission Control Protocol (TCP)/Internet Protocol (IP)”. In order to make possible a uniform processing of data, many data are present in a uniform format, the so-called Hypertext Markup Language (HTML) format.
It is furthermore known from Fundamentals for the World Wide Web to search for given data on the WWW using a WWW browser, and to display these data on a monitor. Such a WWW browser and a computer program implementing the WWW browser are known from Fundamentals for the World Wide Web.
These data can be transmitted in the context of a service which can be requested by a computer on the communication network. Such a service is, for example, a provision of information. An individual computer (user) can then request the service from another individual computer (server) over the communication network. In the context of the service, data are transmitted between the user and the server over the communication network.
It is furthermore known from Fundamentals for the World Wide Web that a computer which makes data available on the communication network and from which data can be requested is such a server.
A communication between a user and a server in which the user requests a service from the server and the server fulfills this request will be termed a session. Correspondingly, a communication between a user and a server on the WWW is termed an Internet session. In a user's Internet session, an item of information which describes the Internet session is stored at the selected server in a so-called “log file”. The information includes, for example, an identification of the user and a duration of the Internet session. Such an Internet session, described by the information, can be interpreted as a state of an “internet session” system. The information would in this case contain state quantities of the system.